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LXXVIII. The Theory of X-Ray Reflexion. Part II. > By 

 C. G. Dak win, M.A., Lecturer in Mathematical Physics in 

 the University of Manchester* . 



1. TN the First Part of this paper f formulae were obtained 

 -L giving the intensity of reflexion of X-rays by a 

 crystal, and by a discussion of the results of experiment £ it 

 was concluded that a factor had been neglected which in 

 fact must be of some importance, and that to represent the 

 case at all accurately an improved theory was necessary. 

 It was indicated that the factor to be included is the influence 

 of the vibration of each atom on that of the others. If this 

 is not done, cases will present themselves in which the con- 

 serv ation of energy is apparently violated. The experiment 

 which was discussed is one of these cases. In the present 

 paper this mutual influence is allowed for and a revised 

 formula is found for the reflexion from a crystal. Com- 

 parison with experiment shows that the new formula is no 

 better able than the old to account for the observed strength 

 of reflexion. It appears, however, that this may be attri- 

 buted to the fact that in all crystals there is a considerable 

 amount of distortion, so that there are a great many separate 

 small regions in which reflexion takes place. As a conse- 

 quence of this fact it will be deduced that, constant factors 

 apart, the old reflexion formulaa may be allowed to stand. 

 We shall first of all deal with the reflexion from a perfect 

 crystal. 



2. Reflexion from one Plane, 



In the earlier work the procedure was first to calculate 

 the reflexion from a single plane of atoms and then to com- 

 bine the effects of the different planes. The amplitude of 

 the reflexion from one plane was represented by a coefficient 

 — iq, where q is made up in the following way. A wave 

 of unit amplitude and length 2ir/k falls on an atom. Let 

 f(yjr, k) e~ ikr /r be the amplitude of the wave it scatters, 

 measured at a distance r in a direction inclined at angle ijr 

 to the direction of the incident wave. In addition to >|r and k t 

 f will depend on the direction of polarization of the incident 

 wave. Let N be the number of atoms per c.c. (for the 

 present we shall suppose them all identical) and a the dis- 

 tance between successive planes; then Na is the areal density 



* Communicated by Prof. Sir Ernest Rutherford, F.E.S. 

 t Darwin, Phil. Mag. vol. xxvii. p. 315 (1914). 

 X Loc. cit. p. 331. 



